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Calculating the Expectation and Variance of the Present Value for a Random Profit Stream of Uncertain Duration

Abstract : We derive the mean and variance of the random discounted sum [[[sigma].sup.N].sub.n=1] [[theta].sup.n][X.sub.n], when N is uncertain, as are the [X.sub.n]'s. This quantity arises in applications involving random cash-flows over an uncertain number of years. One such application is R&D projects, where both the magnitude and duration of cash-flows are uncertain at the time of investment decision. Previous models have assumed cash-flow duration to be certain. We relax this assumption. We then specialize these results to geometric, mixed-geometric and Poisson distributions of the cash-flow duration.
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Submitted on : Sunday, December 4, 2011 - 7:23:55 PM
Last modification on : Tuesday, December 18, 2012 - 2:03:27 PM

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Thomas B. Astebro, Yigal Gerchak. Calculating the Expectation and Variance of the Present Value for a Random Profit Stream of Uncertain Duration. Engineering Economics, Technologija, 2000, 45 (4), pp.339-349. ⟨10.1080/00137910008967557⟩. ⟨hal-00648005⟩

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